To find the limit as x approaches infinity of the given expression, we first simplify the expression:

(3n^2 + 4n - 1)/(3n^2 + 2n + 7)^(2n + 5)

As n approaches infinity, we see that the highest power of n in the numerator and the denominator is n^2. Therefore, we divide every term by n^2 to simplify further:

(3 + 4/n - 1/n^2)/(3 + 2/n + 7/n^2)^(2n + 5)

Since n is approaching infinity, the terms with 4/n and 2/n in the numerator and denominator approach 0. Therefore, our expression simplifies to:

(3 + 0 - 0)/(3 + 0 + 7)^(2n + 5)
(3)/(10)^(2n + 5)

As n approaches infinity, the expression (10)^(2n + 5) becomes increasingly large and tends towards infinity. Therefore, the limit of the given expression as x approaches infinity is:

3/∞ = 0